At Binion's tonight I was involved in a hand that got checked down on all three betting rounds after the flop. I won it with the low end of a straight. I didn't bet because by the river there were four hearts on the board, I didn't have one, and I was out of position against two other opponents.

When the hands were revealed, a player not involved said, "It's amazing that nobody had a heart!"

Apparently his definition of "amazing" and mine vary by a large degree.

Let's ignore the self-selection that usually occurs with poker hands by sequential betting (i.e., when the flop contains two hearts, players with one or two hearts as hole cards are more likely to continue playing than those with none), because here there was no such filtering action. What we are left with is the question of how likely it is that there is at least one heart to be found among six random cards (the hole cards of three players), given that four hearts are seen among the community cards. I will assume that before the flop, nobody is more selective for playing hearts than for any other suit.

We have 47 cards not on the board, which must include 9 hearts. So any individual card chosen at random has a 9/47 chance of being a heart, or 0.191. We use that as the value of p in a binomial calculation. My favorite binomial calculating tool is here. Using it, I learn that the probability of there being exactly one heart in a randomly selected group of six cards, under the circumstances described, is 0.40, or 40%. The probably of there being exactly two hearts among the six cards is 23%. Three hearts is 7%. Four hearts is 1%. Five and six hearts are vanishingly rare, accounting for only about 0.1% combined, so we can ignore those conditions.

In other words, the combined probability of there being at least one heart among the six down cards held by three players, when there are four hearts on the board, is about 72%. That means that about 28% of the time, none of the three players will have a heart. We experienced a condition that will occur 28% of the time--more than one time out of four. Not exactly a rarity. And this doofus considers that to be "amazing"?

Even if there were four players, and thus eight cards to account for, the probability that nobody has a heart is about 18%--again, not exactly a finding incredible enough to write home about. With five players, it's 12%; with six players 8%, with seven players 5%; with eight players 3.4%; with nine players 2.2%; and with ten players 1.4%. Those last two are about what it would take for me to be impressed that something truly out of the ordinary had occurred. But I still wouldn't call it anywhere near "amazing"--just kind of unusual.

I guess some people are a whole lot more easily impressed by minor coincidences than I am.

I hadn't played at Binion's in nearly three months, so when it was time to set out for a game this evening and I didn't really feel like driving anywhere, it was the obvious target. (It's a ten-minute walk from my apartment.) Glad I did--it turned into a very profitable session.

I discovered that Binion's has continued its recent trend of issuing commemorative poker chips, as seen above. Labor Day and Halloween are obvious targets. I'm not sure what the third one is commemorating, other than T&A.

At the table I ran into a reader, name of Eric--from Cleveland, where I changed planes on my trip home Monday. (Lovely city--from the air, anyway.) He recognized me because I was wearing the hoodie sweatshirt that Cardgrrl gave me last month. He and I were involved in a hand that proved interesting. He raised from early position. I called on the button with Kh-Qh. Both blinds called, too. Flop was A-K-Q with two diamonds. Small blind bet $10, big blind called, Eric called. I raised to $40. I knew there was a fair chance I was already beat by a higher two pair, a set, or a straight, but I wanted to find out where things stood.

I found out fast. Small blind pushed all in. Big blind folded. Eric moved all in. I decided one of them had a set and the other J-10 for the straight. I folded. I was right on both counts. Unfortunately, Eric's A-A for the flopped top set was in bad shape, he didn't improve to a full house, and left empty-handed. That's the way it goes sometimes. I felt lucky to have escaped losing only $50 or so. It's weird to flop two pair and be in third place, but as it turned out I was drawing dead to running kings or queens for quads, or J-10 for a straight on the board and a three-way chop.

(Eric, I sympathize. If you haven't read this old post of mine, it's probably worth a few minutes of your time. You'll find a very familiar-sounding story there. It was just about the worst 20 minutes of poker I've ever experienced.)

There were other strange and/or interesting things to be seen at Binion's tonight, which I don't think need further commentary, just photos:

Thursday, October 29, 2009

I was at the Clark County Library today. As I passed by the shelves of non-circulating reference works, something very familiar caught my eye. There, among the various directories, etc., was Super System: A Course in Power Poker, by Doyle Brunson.

At the final table of the Mookie tonight we witnessed this unusual hand. This screen shot makes it look like I was involved, though I wasn't. I folded pre-flop. I don't remember who else played it, but it was won by a bet on the turn without a showdown.

It made me wonder how rare it is to see four of a kind in the first four board cards. Let's find out, shall we?

As I have discussed before, there are 19,600 possible flops, given that I am holding two cards that are therefore unavailable. How many of these flops will be three of a kind? Well, there are 11 ranks of cards not matching the ones that I'm holding (assuming I don't have a pocket pair). For each of those, there are six possible combinations of the suits that could constitute a single-rank flop. That's 66. I'm going to neglect the other two ranks, because even if the other three come on the flop, it's not going to be quads on the turn as shown in the example hand in question.

66/19,600 = 0.00337, so about three out of a thousand times you'll see a flop of a single rank.

What about the turn being the fourth one? There are now five cards accounted for, so 47 left in the deck. Only one of them fits the bill, so only one time in 47 that we have flopped trips on the board will we then see quads on the turn. 0.00337/47 = 0.000072. Inverting that, the result is that only one time in about 13,958 hands will the cards turn out to have four of a kind on the board at the turn, as shown above.

That's rare enough to be worth gawking at for a moment or two, I think.

Why the end of the world? Because in the course of just five consecutive Wednesdays, I have played the Mookie four times, coming in second on September 30, then winning it on October 7, final table but no cash on October 14, skipped it October 21, then won it again tonight. This is both an unexpected and unprecedented sort of streak for me--so unusual, so inexplicable that it must be considered a sign of the apocalypse. As readers know by now, tournaments aren't really my thing--especially online ones.

I felt like I played reasonably well, though not spectacularly by any means. I got lucky early on and hit all sorts of flops, allowing me to build up a decent stack that kept me afloat through the rocky bits. For example, there was this hand just ten minutes in:

I believe that I only had all my chips in with the worst of it and had to get lucky on two occasions. This next hand was the first of them. VBPro7 had been stealing my blinds relentlessly, so I decided it was time to play back at him:

His call on the flop was either genius or insane--I'm still not sure which. But either way, I got very lucky to catch a six-outer on him.

At the time I made that move, I thought it was possible that she had missed the board completely (and might have just been on a random blind steal to begin with), though I knew that with the pre-flop raise she could easily have a king. When she took so long to decide whether to call or fold, I became convinced that she did, in fact, have a king. (She still hasn't told me, so I don't know.) But I thought had pretty good fold equity even if she did have one pair, and the pair and flush draw gave me plenty of outs in the event that she called.

Of course, it is mandatory that I win at least one hand with the Deuce-Four:

I don't know what Cardgrrl had there, but she claims that she was ahead. (I showed the hand, of course.) Not that it matters, since a 5 was inevitably coming to give me the straight and the win.

Now we're down to the final table, six players left, four to be paid, when this hand comes up against CK:

In the replay it looks like it went quick, but it actually took some time. Unless she was just posturing (which I think unlikely), she had a real decision there. That, plus a cryptic comment in the chat box after the hand (which I showed), gave me the sick feeling that I beat the mighty Deuce-Four there. If so, may CK and the poker gods forgive me! Also if so, phenomenal laydown, CK.

OK, so now we're five-handed, on the bubble, and I'm the second to shortest stack. I remember what Daniel Negreanu said about bubble boys, and I decided to go for the gusto rather than sneak into the money like a little rat. That decision was made much easier when I found QQ in the small blind. The raiser here was the monster stack, and had been abusing the bubble mercilessly (as, of course, he should). But here he made a really questionable call, probably inspired by the thought that he had plenty of chips to spare. The result was to give me a crucial double-up:

A short time later I got my biggest advance in chips of the entire tournament when I flopped a set on an essentially draw-free board, in position against the preflop raiser, who was the only person with enough chips to double me up--in other words, kind of a perfect storm:

But in classic fashion (for me, anyway), I held on to this bounty of chips for a mere three minutes before donking them off. In the interim the bubble had burst:

Sigh. Why must I always have a blow-up like that? It's like I subconsciously feel I don't deserve to have the big chip lead, so I have to find a way to give them to the other players.

Anyway, by the time we got down to the final three of us, I was the short stack, and had my second instance of getting ridiculously lucky after all the money was in:

If I can be legitimately proud of any part of the tournament, it would have to be the heads-up play. I started with a 3:1 chip deficit (78K to 27K), but chipped away at the lead pretty persistently, until I got an opportunity for a big move forward by calling my opponent down with second pair:

One could certainly argue for being more aggressive there, but I was out of position. Furthermore, I believed that Jestocost had been trying to get me to commit all my chips badly and go for the knockout, and I was pretty determined to exercise pot control until I was in a clearly dominating spot. Since I didn't believe he had an ace, with no preflop raise, I was content to play this one passively and cautiously, and it worked out for me.

Just eight minutes later, I got The Big Hand, the one that I had been waiting for, the one that turned it all around:

That was pretty much all she wrote. Then it was just a matter of not getting chip-drunk and blowing it again, but instead waiting for a spot to land the final blow. The chip stacks went up and down a bit, but were close to the same as at the end of that hand when I found what seemed to be a good spot to try for the win:

And that was the end of it.

Nothing about this little streak changes anything. I'm still a mediocre tournament player and mediocre online player. As you can see, I'm still prone to stupid moves. But it's nice to have gotten a little bit of luck to combine with a few moments of my A-game in nearly consecutive weeks of this running tournament series. It's not big money or glory, but I'm pleased with how things have turned out here.

So I just wrote the previous post. It's up. I'm proofreading it. It occurs to me that I once heard Mike Sexton make the same mistake (saying "reraise" when it was just a raise). I think that that would make a nice extra touch to add to the post. I start trying to see if I can remember which World Poker Tour event it was where I heard Sexton's gaffe. Then another thought starts creeping into the old noggin: Didn't I write a blog post about that when it happened? A quick search reveals not only that I did, but that I did a whole rant about the "reraise" thing back in May, 2008, in which I detailed the circumstances of his comment.

And now I just repeated myself, except that it probably wasn't as good the second time around.

On Sunday I was in a 14-player home tournament with Cardgrrl. I busted out and joined a cash game on the side, while she kept playing. (She won it, not too surprisingly, though she has so far been too modest to note that fact in her own blog.) I lost the biggest pot of the day (something like $70, which was massive, given that the stakes were $0.10/$0.20!) in one of the most annoying ways possible. Four of us checked it around on the river. I had top two pair, but didn't bet because the river put a fourth heart on the board, and I didn't have one. I showed my cards. Two of the others mucked. The last one made a dejected face and pushed his cards forward a few inches, face down, as if to muck. (This is a player-dealt game, and there was no clearly defined muck area.) Just then, a bozo at the far end of the table, not involved in the hand, said, "Nobody has a heart?" The fourth player, apparently not having noticed the four-flush on the board, then picked up his cards again, discovered that he had the ten of hearts, showed, and took the pot.

Why didn't I write a whiny blog post about this at the time? Because it was virtually identical to an incident I related here (fifth story) about a hand at Bill's, just over a year ago. I thought about recounting Sunday's hand in detail, complete with a rant about how such a stray comment egregiously violates the rule about not talking about the hand in progress, as well as the "one player to a hand" principle. (When you help one player in poker, you almost inevitably hurt another at the same time.) But why bother, when I've already done that post before? At least in that case I managed to remember having told the story before.

So this is one of the problems of having been blogging quite prolifically for a hair under three years now. (My first post was made on October 30, 2006. Happy early anniversary to me!) I have already tackled a hefty percentage of all the things I can think of to talk about. New things happen to me at the poker table with a much lower frequency than when I was first in Vegas. It's not exactly true that I've seen it all and done it all, but I've certainly seen, done, and written about a whole helluva lot more than I had back then. There are fewer novel thoughts and novel experiences to share with readers.

That leaves me the dilemma of repeating myself intentionally (figuring that not everybody has been reading all along), repeating myself unintentionally (as happened earlier today), just putting up pointers to an old post with a note like "this happened to me again," or just letting things go silently. I'm not sure that any of those is the optimal solution, though they'll probably all be deployed once in a while.

If you catch me telling virtually the same story a second--or even third--time, forgive me. It might be deliberate. Or it might be senility setting in.

I'm catching up with last week's World Series of Poker broadcast. In one hand, the action on the turn card is Phil Ivey checks, Joseph Ward bets 200K, Ivey check-raises to 600K. But in the voiceover, Lon McEachern says, "Ivey with a reraise here to six hundred thousand."

Reraise? How can there be a reraise when there wasn't a raise first? A raise after a previous raise is a reraise; a raise after a bet is just a raise.

People make this mistake all the time. Somebody bets the flop, and the next player announces, "Reraise." Even people with enough experience to know better screw this up. One of my best friends does it on a fairly regular basis. And I just don't get it. I essentially never announce reraise. There is no situation in which one needs to use it. The word raise works perfectly well for every occasion where reraise is acceptable. So why not just eliminate the unnecessary word from one's working vocabulary, stick to raise for everything, and never risk making an embarrassing mistake?

It has nothing to do with poker. The title tells all: "Something beautiful I saw today." The author posts a photograph of and/or link to something beautiful seen that day. One post a day, with minimal reading needed. It will add just a little touch of pleasantness to your life, with virtually no time investment. How can you resist that bargain?

I moved all the pictures I took on my recent trip from the camera to the computer, and have now uploaded most of them (I left out the duplicates, blurry and badly exposed ones, etc.) to my Picasa album.

One of the most spectacular landmarks in D.C. is the National Cathedral. Cardgrrl happens to live just a stone's throw away from it, so I went over on Saturday and looked around. It's a lovely building and grounds, with grand views of the city all around. See here.

Six months ago I put up post #1500. Actually, it slipped by before I noticed it. At that point I decided to abandon the notices for every hundredth post and move instead to one every 500.

Well, the next planned milestone slipped by me, too--by a long way. The 2000th post was apparently this one, posted automatically right after I had arrived in D.C. almost two weeks ago. I was kinda busy and distracted--though in very pleasant ways--so I think I can be forgiven. This one appears to actually be #2019. Oh well.

I continue to be flattered, honored, and not a little surprised that so many of you tune in to see what I'm up to and what I have to say about it. I hope to continue to entertain and inform you to the best of my ability for a long time to come.

Cardgrrl and I had another non-poker day today. It was spent at the home of her closest friends, a husband-and-wife pair that she has known since college days. I had exchanged some correspondence with them in advance, and had anticipated that meeting them would be one of the best parts of the trip. I was right. They proved to be a completely delightful couple that I hope will be in my circle of friends for a long time to come.

The highlight of the visit was playing a game that Cardgrrl has played with them (and their two teenage sons, one of which was there, the other of which is off to college) frequently in the past: "Apples to Apples." This is absolutely one of the best games I've ever enountered. It is simple in premise, virtually instant to learn, fast-paced, funny, creative, and endlessly entertaining. Each player has seven red cards, on each of which is the name of a person, place, or thing (James Dean, oil spill, the Eiffel Tower, high school reunion, the ozone layer, babies, loan shark, girlfriends). One player, acting as judge, selects a green card from the pack. The green cards contain a concept or quality (silly, fake, manly, touchy-feely, clean, demanding, etc.). Players select from their red cards the one that they think the judge will decide best fits the category or characteristic specified on the green card. The judge can make the decision on any basis he or she wishes (the most literally correct, the funniest, the most ironic, or even random). The person whose red card is selected by the judge keeps that green card, and the first player with seven green cards wins.

I won twice in a row. And I have to tell you, it wasn't even close. In the first game, nobody had more than three when I hit seven. In the second somebody had gotten to five, but none of the others had more than three.

In other words, I crushed. (Here's that "insufferable" thing again that Cardgrrl was talking about. Don't worry--it won't last long.)

A large part of it is luck--having cards that perfectly fit and that are kind of obvious winners. E.g., I had "First man on the moon" when the category was "Technological." Hard to top that. (I also had "Skinheads" when the green card said "Hostile," and thought it was a shoe-in, but lost a close decision to "Attack on Pearl Harbor.") But some of the game is also getting inside the head of the judge and anticipating what he or she will find compelling. E.g., I submitted "Eiffel Tower" for the "Manly" green card, thinking that the judge (the teenage son) would find the phallic symbolism an irresistibly cutesy way to make his decision--and he did. Similarly, I guessed that our hostess, then serving as judge, would appreciate the lateralness of "talk radio" submitted for the "chewy" green card--i.e., topics for discussion on the radio being stuff to chew on, as in "chew the fat." She did, and on that basis.

Do you see poker parallels here? I sure do (though, of course, I tend to see them everywhere, so it's not saying much). You have to be able to see the game from the perspective of somebody else in order to be successful. I won a green card by correctly anticipating that our host would think "Corvettes" were more "Neat" than whatever others were submitting, but I would not have made the same choice if, say, Cardgrrl had been the judge that round--just as I will be more inclined to play a tricky little hand like 5-7 offsuit against an opponent that I believe has a big pair and will get too married to it than against a cautious player who is good at smelling traps and getting out of them, and will be more inclined to fire the three-barrel bluff at the overly nitty play-only-the-nuts guy than at the calling station.

A couple of years ago I briefly was part of a small group of players who shared difficult poker hands via email discussion. It didn't last long. I confess that I didn't contribute much. (Some of them are readers--so, sorry, guys.) Here's why: Every time I thought about submitting a hand for consideration, it boiled down to a question of deciding how this particular player would react to a bluff, value-bet, or whatever, or what cards he might have in this specific situation. But how to convey by email what information I had on that point? Consider, for example, this hand, which took me forever to write up, because of trying to explain everything I had gathered about my opponent, how previous hands had played out, what his emotional state and image of me likely were, etc. I just couldn't find the time or inclination to type out that level of detail very often. But that's just what one needs in order to make good decisions in poker--particularly in no-limit games--whether on the spot or after the fact. Who you are playing against is an enormous part of every decision you have to make.

As for "Apples to Apples," if we're being honest, most of my success today was the proverbial beginner's luck of having superior cards. After all, my four opponents not only know each other much better than I know any of them (or they me), but they have played this exact game against each other many times. So I'm not going to fool myself into thinking that it was some poker-honed, ultra-superior, mind-penetrating radar that brought the wins. But it was definitely in my thoughts the whole time that seeing things as other players see them was a crucial element to that game, as well as to the one with which I'm more familiar.

Cardgrrl and I are going to a live deep-stack tournament tomorrow, probably to be followed by a cash game. I hope that I am able to carry over at least a little bit of the good fortune I had today, and also remember how useful it can be to get inside the other players' heads.

About Me

It's a little hard to say this, because I'm not used to it yet, but I suppose that I'm a professional poker player. I moved to Vegas intending to get a job as a poker dealer, but while waiting to get hired, I spent the days playing poker instead of dealing it, and soon found that I was able to keep the bills paid. So I've just kept on doing it. I play Hold'em exclusively, usually no-limit, and most commonly $1-2 or $1-3, with occasional forays into $2-5 territory. I play tournaments on-line once in a while, but for some reason that I haven't entirely figured out, I'm much more successful playing at casinos than on the Internet, and much better at cash games than tournaments.
You can contact me via email: it's rakewell1 at yahoo dotdotdot com.